Impossible figures are striking examples of inconsistency between global and local perceptual structure (see Figure 1a). These images tend to attract our attention and interest for extended periods of time as we try to resolve the component parts, perhaps because each part of an impossible figure in isolation is locally possible, but the overall spatial configuration does not yield a globally coherent 3D object. In order to investigate whether structural "impossibility" was considered an important perceptual property of depicted objects, we used a category formation task in which subjects were asked to divide pictures of shapes into groups that seemed most natural to them. Category formation is usually unidimensional, i.e., sorting is dominated by a single perceptual property, and so it serves as a measure of which features or dimensions are most salient. In Experiment 1, subjects received a set of 12 line drawings, half of which depicted possible and half impossible objects (Figure 1a). Very few subjects grouped the figures by impossibility on the first try, and only half did so after multiple attempts at sorting. Experiment 2 investigated other global properties of figures, such as symmetry and complexity (Figure 1b and 1c). Subjects readily sorted objects by complexity, but seldom by symmetry. In Experiment 3, subjects were asked to draw each of the figures before sorting them, which had only a minimal effect on facilitating categorization. Finally, in Experiment 4, subjects were explicitly instructed to divide the shapes by symmetry or impossibility. Following the prompt, performance on the categorization task was perfect for symmetry, but not for impossibility. Although global properties of figures seem extremely important to our perception, the results suggest that some of these cues are not salient for about half of observers.